{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 锚框\n",
    "\n",
    "目标检测算法通常会在输入图像中采样大量的区域，然后判断这些区域中是否包含我们感兴趣的目标，并调整区域边缘从而更准确地预测目标的真实边界框（ground-truth bounding box）。不同的模型使用的区域采样方法可能不同。这里我们介绍其中的一种方法：它以每个像素为中心生成多个大小和宽高比（aspect ratio）不同的边界框。这些边界框被称为锚框（anchor box）。我们将在后面基于锚框实践目标检测。\n",
    "\n",
    "首先，导入本节需要的包或模块。这里我们新引入了`contrib`包，并修改了NumPy的打印精度。由于`NDArray`的打印实际调用NumPy的打印函数，本节打印出的`NDArray`中的浮点数更简洁一些。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "1"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import d2lzh as d2l\n",
    "from mxnet import contrib, gluon, image, nd\n",
    "import numpy as np\n",
    "np.set_printoptions(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 生成多个锚框\n",
    "\n",
    "假设输入图像高为$h$，宽为$w$。我们分别以图像的每个像素为中心生成不同形状的锚框。设大小为$s\\in (0,1]$且宽高比为$r > 0$，那么锚框的宽和高将分别为$ws\\sqrt{r}$和$hs/\\sqrt{r}$。当中心位置给定时，已知宽和高的锚框是确定的。\n",
    "\n",
    "下面我们分别设定好一组大小$s_1,\\ldots,s_n$和一组宽高比$r_1,\\ldots,r_m$。如果以每个像素为中心时使用所有的大小与宽高比的组合，输入图像将一共得到$whnm$个锚框。虽然这些锚框可能覆盖了所有的真实边界框，但计算复杂度容易过高。因此，我们通常只对包含$s_1$或$r_1$的大小与宽高比的组合感兴趣，即\n",
    "\n",
    "$$(s_1, r_1), (s_1, r_2), \\ldots, (s_1, r_m), (s_2, r_1), (s_3, r_1), \\ldots, (s_n, r_1).$$\n",
    "\n",
    "也就是说，以相同像素为中心的锚框的数量为$n+m-1$。对于整个输入图像，我们将一共生成$wh(n+m-1)$个锚框。\n",
    "\n",
    "以上生成锚框的方法已实现在`MultiBoxPrior`函数中。指定输入、一组大小和一组宽高比，该函数将返回输入的所有锚框。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "2"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "561 728\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(1, 2042040, 4)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "img = image.imread('../img/catdog.jpg').asnumpy()\n",
    "h, w = img.shape[0:2]\n",
    "\n",
    "print(h, w)\n",
    "X = nd.random.uniform(shape=(1, 3, h, w))  # 构造输入数据\n",
    "Y = contrib.nd.MultiBoxPrior(X, sizes=[0.75, 0.5, 0.25], ratios=[1, 2, 0.5])\n",
    "Y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们看到，返回锚框变量`y`的形状为（批量大小，锚框个数，4）。将锚框变量`y`的形状变为（图像高，图像宽，以相同像素为中心的锚框个数，4）后，我们就可以通过指定像素位置来获取所有以该像素为中心的锚框了。下面的例子里我们访问以（250，250）为中心的第一个锚框。它有4个元素，分别是锚框左上角的$x$和$y$轴坐标和右下角的$x$和$y$轴坐标，其中$x$和$y$轴的坐标值分别已除以图像的宽和高，因此值域均为0和1之间。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "3"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "[0.06 0.07 0.63 0.82]\n",
       "<NDArray 4 @cpu(0)>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boxes = Y.reshape((h, w, 5, 4))\n",
    "boxes[250, 250, 0, :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "为了描绘图像中以某个像素为中心的所有锚框，我们先定义`show_bboxes`函数以便在图像上画出多个边界框。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "4"
    }
   },
   "outputs": [],
   "source": [
    "# 本函数已保存在d2lzh包中方便以后使用\n",
    "def show_bboxes(axes, bboxes, labels=None, colors=None):\n",
    "    def _make_list(obj, default_values=None):\n",
    "        if obj is None:\n",
    "            obj = default_values\n",
    "        elif not isinstance(obj, (list, tuple)):\n",
    "            obj = [obj]\n",
    "        return obj\n",
    "\n",
    "    labels = _make_list(labels)\n",
    "    colors = _make_list(colors, ['b', 'g', 'r', 'm', 'c'])\n",
    "    for i, bbox in enumerate(bboxes):\n",
    "        color = colors[i % len(colors)]\n",
    "        rect = d2l.bbox_to_rect(bbox.asnumpy(), color)\n",
    "        axes.add_patch(rect)\n",
    "        if labels and len(labels) > i:\n",
    "            text_color = 'k' if color == 'w' else 'w'\n",
    "            axes.text(rect.xy[0], rect.xy[1], labels[i],\n",
    "                      va='center', ha='center', fontsize=9, color=text_color,\n",
    "                      bbox=dict(facecolor=color, lw=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "刚刚我们看到，变量`boxes`中$x$和$y$轴的坐标值分别已除以图像的宽和高。在绘图时，我们需要恢复锚框的原始坐标值，并因此定义了变量`bbox_scale`。现在，我们可以画出图像中以(250, 250)为中心的所有锚框了。可以看到，大小为0.75且宽高比为1的锚框较好地覆盖了图像中的狗。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "5"
    }
   },
   "outputs": [
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    "## 交并比\n",
    "\n",
    "我们刚刚提到某个锚框较好地覆盖了图像中的狗。如果该目标的真实边界框已知，这里的“较好”该如何量化呢？一种直观的方法是衡量锚框和真实边界框之间的相似度。我们知道，Jaccard系数（Jaccard index）可以衡量两个集合的相似度。给定集合$\\mathcal{A}$和$\\mathcal{B}$，它们的Jaccard系数即二者交集大小除以二者并集大小：\n",
    "\n",
    "$$J(\\mathcal{A},\\mathcal{B}) = \\frac{\\left|\\mathcal{A} \\cap \\mathcal{B}\\right|}{\\left| \\mathcal{A} \\cup \\mathcal{B}\\right|}.$$\n",
    "\n",
    "\n",
    "实际上，我们可以把边界框内的像素区域看成是像素的集合。如此一来，我们可以用两个边界框的像素集合的Jaccard系数衡量这两个边界框的相似度。当衡量两个边界框的相似度时，我们通常将Jaccard系数称为交并比（intersection over union，IoU），即两个边界框相交面积与相并面积之比，如图9.2所示。交并比的取值范围在0和1之间：0表示两个边界框无重合像素，1表示两个边界框相等。\n",
    "\n",
    "![交并比是两个边界框相交面积与相并面积之比](../img/iou.svg)\n",
    "\n",
    "在本节的剩余部分，我们将使用交并比来衡量锚框与真实边界框以及锚框与锚框之间的相似度。\n",
    "\n",
    "\n",
    "\n",
    "## 标注训练集的锚框\n",
    "\n",
    "\n",
    "在训练集中，我们将每个锚框视为一个训练样本。为了训练目标检测模型，我们需要为每个锚框标注两类标签：一是锚框所含目标的类别，简称类别；二是真实边界框相对锚框的偏移量，简称偏移量（offset）。在目标检测时，我们首先生成多个锚框，然后为每个锚框预测类别以及偏移量，接着根据预测的偏移量调整锚框位置从而得到预测边界框，最后筛选需要输出的预测边界框。\n",
    "\n",
    "\n",
    "我们知道，在目标检测的训练集中，每个图像已标注了真实边界框的位置以及所含目标的类别。在生成锚框之后，我们主要依据与锚框相似的真实边界框的位置和类别信息为锚框标注。那么，该如何为锚框分配与其相似的真实边界框呢？\n",
    "\n",
    "\n",
    "假设图像中锚框分别为$A_1, A_2, \\ldots, A_{n_a}$，真实边界框分别为$B_1, B_2, \\ldots, B_{n_b}$，且$n_a \\geq n_b$。定义矩阵$\\boldsymbol{X} \\in \\mathbb{R}^{n_a \\times n_b}$，其中第$i$行第$j$列的元素$x_{ij}$为锚框$A_i$与真实边界框$B_j$的交并比。\n",
    "首先，我们找出矩阵$\\boldsymbol{X}$中最大元素，并将该元素的行索引与列索引分别记为$i_1,j_1$。我们为锚框$A_{i_1}$分配真实边界框$B_{j_1}$。显然，锚框$A_{i_1}$和真实边界框$B_{j_1}$在所有的“锚框—真实边界框”的配对中相似度最高。接下来，将矩阵$\\boldsymbol{X}$中第$i_1$行和第$j_1$列上的所有元素丢弃。找出矩阵$\\boldsymbol{X}$中剩余的最大元素，并将该元素的行索引与列索引分别记为$i_2,j_2$。我们为锚框$A_{i_2}$分配真实边界框$B_{j_2}$，再将矩阵$\\boldsymbol{X}$中第$i_2$行和第$j_2$列上的所有元素丢弃。此时矩阵$\\boldsymbol{X}$中已有两行两列的元素被丢弃。\n",
    "依此类推，直到矩阵$\\boldsymbol{X}$中所有$n_b$列元素全部被丢弃。这个时候，我们已为$n_b$个锚框各分配了一个真实边界框。\n",
    "接下来，我们只遍历剩余的$n_a - n_b$个锚框：给定其中的锚框$A_i$，根据矩阵$\\boldsymbol{X}$的第$i$行找到与$A_i$交并比最大的真实边界框$B_j$，且只有当该交并比大于预先设定的阈值时，才为锚框$A_i$分配真实边界框$B_j$。\n",
    "\n",
    "\n",
    "如图9.3（左）所示，假设矩阵$\\boldsymbol{X}$中最大值为$x_{23}$，我们将为锚框$A_2$分配真实边界框$B_3$。然后，丢弃矩阵中第2行和第3列的所有元素，找出剩余阴影部分的最大元素$x_{71}$，为锚框$A_7$分配真实边界框$B_1$。接着如图9.3（中）所示，丢弃矩阵中第7行和第1列的所有元素，找出剩余阴影部分的最大元素$x_{54}$，为锚框$A_5$分配真实边界框$B_4$。最后如图9.3（右）所示，丢弃矩阵中第5行和第4列的所有元素，找出剩余阴影部分的最大元素$x_{92}$，为锚框$A_9$分配真实边界框$B_2$。之后，我们只需遍历除去$A_2, A_5, A_7, A_9$的剩余锚框，并根据阈值判断是否为剩余锚框分配真实边界框。\n",
    "\n",
    "![为锚框分配真实边界框](../img/anchor-label.svg)\n",
    "\n",
    "\n",
    "现在我们可以标注锚框的类别和偏移量了。如果一个锚框$A$被分配了真实边界框$B$，将锚框$A$的类别设为$B$的类别，并根据$B$和$A$的中心坐标的相对位置以及两个框的相对大小为锚框$A$标注偏移量。由于数据集中各个框的位置和大小各异，因此这些相对位置和相对大小通常需要一些特殊变换，才能使偏移量的分布更均匀从而更容易拟合。设锚框$A$及其被分配的真实边界框$B$的中心坐标分别为$(x_a, y_a)$和$(x_b, y_b)$，$A$和$B$的宽分别为$w_a$和$w_b$，高分别为$h_a$和$h_b$，一个常用的技巧是将$A$的偏移量标注为\n",
    "\n",
    "$$\\left( \\frac{ \\frac{x_b - x_a}{w_a} - \\mu_x }{\\sigma_x},\n",
    "\\frac{ \\frac{y_b - y_a}{h_a} - \\mu_y }{\\sigma_y},\n",
    "\\frac{ \\log \\frac{w_b}{w_a} - \\mu_w }{\\sigma_w},\n",
    "\\frac{ \\log \\frac{h_b}{h_a} - \\mu_h }{\\sigma_h}\\right),$$\n",
    "\n",
    "其中常数的默认值为$\\mu_x = \\mu_y = \\mu_w = \\mu_h = 0, \\sigma_x=\\sigma_y=0.1, \\sigma_w=\\sigma_h=0.2$。如果一个锚框没有被分配真实边界框，我们只需将该锚框的类别设为背景。类别为背景的锚框通常被称为负类锚框，其余则被称为正类锚框。\n",
    "\n",
    "\n",
    "下面演示一个具体的例子。我们为读取的图像中的猫和狗定义真实边界框，其中第一个元素为类别（0为狗，1为猫），剩余4个元素分别为左上角的$x$和$y$轴坐标以及右下角的$x$和$y$轴坐标（值域在0到1之间）。这里通过左上角和右下角的坐标构造了5个需要标注的锚框，分别记为$A_0, \\ldots, A_4$（程序中索引从0开始）。先画出这些锚框与真实边界框在图像中的位置。"
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   ],
   "source": [
    "ground_truth = nd.array([[0, 0.1, 0.08, 0.52, 0.92],\n",
    "                         [1, 0.55, 0.2, 0.9, 0.88]])\n",
    "anchors = nd.array([[0, 0.1, 0.2, 0.3], [0.15, 0.2, 0.4, 0.4],\n",
    "                    [0.63, 0.05, 0.88, 0.98], [0.66, 0.45, 0.8, 0.8],\n",
    "                    [0.57, 0.3, 0.92, 0.9]])\n",
    "\n",
    "fig = d2l.plt.imshow(img)\n",
    "show_bboxes(fig.axes, ground_truth[:, 1:] * bbox_scale, ['dog', 'cat'], 'k')\n",
    "show_bboxes(fig.axes, anchors * bbox_scale, ['0', '1', '2', '3', '4']);"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们可以通过`contrib.nd`模块中的`MultiBoxTarget`函数来为锚框标注类别和偏移量。该函数将背景类别设为0，并令从零开始的目标类别的整数索引自加1（1为狗，2为猫）。我们通过`expand_dims`函数为锚框和真实边界框添加样本维，并构造形状为(批量大小, 包括背景的类别个数, 锚框数)的任意预测结果。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "7"
    }
   },
   "outputs": [],
   "source": [
    "labels = contrib.nd.MultiBoxTarget(anchors.expand_dims(axis=0),\n",
    "                                   ground_truth.expand_dims(axis=0),\n",
    "                                   nd.zeros((1, 3, 5)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "返回的结果里有3项，均为`NDArray`。第三项表示为锚框标注的类别。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "8"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "[[0. 1. 2. 0. 2.]]\n",
       "<NDArray 1x5 @cpu(0)>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "labels[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们根据锚框与真实边界框在图像中的位置来分析这些标注的类别。首先，在所有的“锚框—真实边界框”的配对中，锚框$A_4$与猫的真实边界框的交并比最大，因此锚框$A_4$的类别标注为猫。不考虑锚框$A_4$或猫的真实边界框，在剩余的“锚框—真实边界框”的配对中，最大交并比的配对为锚框$A_1$和狗的真实边界框，因此锚框$A_1$的类别标注为狗。接下来遍历未标注的剩余3个锚框：与锚框$A_0$交并比最大的真实边界框的类别为狗，但交并比小于阈值（默认为0.5），因此类别标注为背景；与锚框$A_2$交并比最大的真实边界框的类别为猫，且交并比大于阈值，因此类别标注为猫；与锚框$A_3$交并比最大的真实边界框的类别为猫，但交并比小于阈值，因此类别标注为背景。\n",
    "\n",
    "\n",
    "返回值的第二项为掩码（mask）变量，形状为(批量大小, 锚框个数的四倍)。掩码变量中的元素与每个锚框的4个偏移量一一对应。\n",
    "由于我们不关心对背景的检测，有关负类的偏移量不应影响目标函数。通过按元素乘法，掩码变量中的0可以在计算目标函数之前过滤掉负类的偏移量。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "9"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "[[0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 1. 1. 0. 0. 0. 0. 1. 1. 1. 1.]]\n",
       "<NDArray 1x20 @cpu(0)>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "labels[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "返回的第一项是为每个锚框标注的四个偏移量，其中负类锚框的偏移量标注为0。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "10"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "[[ 0.00e+00  0.00e+00  0.00e+00  0.00e+00  1.40e+00  1.00e+01  2.59e+00\n",
       "   7.18e+00 -1.20e+00  2.69e-01  1.68e+00 -1.57e+00  0.00e+00  0.00e+00\n",
       "   0.00e+00  0.00e+00 -5.71e-01 -1.00e+00 -8.94e-07  6.26e-01]]\n",
       "<NDArray 1x20 @cpu(0)>"
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     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
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   ],
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 输出预测边界框\n",
    "\n",
    "在模型预测阶段，我们先为图像生成多个锚框，并为这些锚框一一预测类别和偏移量。随后，我们根据锚框及其预测偏移量得到预测边界框。当锚框数量较多时，同一个目标上可能会输出较多相似的预测边界框。为了使结果更加简洁，我们可以移除相似的预测边界框。常用的方法叫作非极大值抑制（non-maximum suppression，NMS）。\n",
    "\n",
    "我们来描述一下非极大值抑制的工作原理。对于一个预测边界框$B$，模型会计算各个类别的预测概率。设其中最大的预测概率为$p$，该概率所对应的类别即$B$的预测类别。我们也将$p$称为预测边界框$B$的置信度。在同一图像上，我们将预测类别非背景的预测边界框按置信度从高到低排序，得到列表$L$。从$L$中选取置信度最高的预测边界框$B_1$作为基准，将所有与$B_1$的交并比大于某阈值的非基准预测边界框从$L$中移除。这里的阈值是预先设定的超参数。此时，$L$保留了置信度最高的预测边界框并移除了与其相似的其他预测边界框。\n",
    "接下来，从$L$中选取置信度第二高的预测边界框$B_2$作为基准，将所有与$B_2$的交并比大于某阈值的非基准预测边界框从$L$中移除。重复这一过程，直到$L$中所有的预测边界框都曾作为基准。此时$L$中任意一对预测边界框的交并比都小于阈值。最终，输出列表$L$中的所有预测边界框。\n",
    "\n",
    "下面来看一个具体的例子。先构造4个锚框。简单起见，我们假设预测偏移量全是0：预测边界框即锚框。最后，我们构造每个类别的预测概率。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "11"
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   },
   "outputs": [],
   "source": [
    "anchors = nd.array([[0.1, 0.08, 0.52, 0.92], [0.08, 0.2, 0.56, 0.95],\n",
    "                    [0.15, 0.3, 0.62, 0.91], [0.55, 0.2, 0.9, 0.88]])\n",
    "offset_preds = nd.array([0] * anchors.size)\n",
    "cls_probs = nd.array([[0] * 4,  # 背景的预测概率\n",
    "                      [0.9, 0.8, 0.7, 0.1],  # 狗的预测概率\n",
    "                      [0.1, 0.2, 0.3, 0.9]])  # 猫的预测概率"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在图像上打印预测边界框和它们的置信度。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "12"
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      "text/plain": [
       "<Figure size 252x180 with 1 Axes>"
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     "metadata": {
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     "output_type": "display_data"
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   ],
   "source": [
    "fig = d2l.plt.imshow(img)\n",
    "show_bboxes(fig.axes, anchors * bbox_scale,\n",
    "            ['dog=0.9', 'dog=0.8', 'dog=0.7', 'cat=0.9'])"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们使用`contrib.nd`模块的`MultiBoxDetection`函数来执行非极大值抑制并设阈值为0.5。这里为`NDArray`输入都增加了样本维。我们看到，返回的结果的形状为(批量大小, 锚框个数, 6)。其中每一行的6个元素代表同一个预测边界框的输出信息。第一个元素是索引从0开始计数的预测类别（0为狗，1为猫），其中-1表示背景或在非极大值抑制中被移除。第二个元素是预测边界框的置信度。剩余的4个元素分别是预测边界框左上角的$x$和$y$轴坐标以及右下角的$x$和$y$轴坐标（值域在0到1之间）。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "13"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "[[[ 0.    0.9   0.1   0.08  0.52  0.92]\n",
       "  [ 1.    0.9   0.55  0.2   0.9   0.88]\n",
       "  [-1.    0.8   0.08  0.2   0.56  0.95]\n",
       "  [-1.    0.7   0.15  0.3   0.62  0.91]]]\n",
       "<NDArray 1x4x6 @cpu(0)>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output = contrib.ndarray.MultiBoxDetection(\n",
    "    cls_probs.expand_dims(axis=0), offset_preds.expand_dims(axis=0),\n",
    "    anchors.expand_dims(axis=0), nms_threshold=0.5)\n",
    "output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们移除掉类别为-1的预测边界框，并可视化非极大值抑制保留的结果。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "attributes": {
     "classes": [],
     "id": "",
     "n": "14"
    }
   },
   "outputs": [
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      "text/plain": [
       "<Figure size 252x180 with 1 Axes>"
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   ],
   "source": [
    "fig = d2l.plt.imshow(img)\n",
    "for i in output[0].asnumpy():\n",
    "    if i[0] == -1:\n",
    "        continue\n",
    "    label = ('dog=', 'cat=')[int(i[0])] + str(i[1])\n",
    "    show_bboxes(fig.axes, [nd.array(i[2:]) * bbox_scale], label)"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "实践中，我们可以在执行非极大值抑制前将置信度较低的预测边界框移除，从而减小非极大值抑制的计算量。我们还可以筛选非极大值抑制的输出，例如，只保留其中置信度较高的结果作为最终输出。\n",
    "\n",
    "\n",
    "## 小结\n",
    "\n",
    "* 以每个像素为中心，生成多个大小和宽高比不同的锚框。\n",
    "* 交并比是两个边界框相交面积与相并面积之比。\n",
    "* 在训练集中，为每个锚框标注两类标签：一是锚框所含目标的类别；二是真实边界框相对锚框的偏移量。\n",
    "* 预测时，可以使用非极大值抑制来移除相似的预测边界框，从而令结果简洁。\n",
    "\n",
    "## 练习\n",
    "\n",
    "* 改变`MultiBoxPrior`函数中`sizes`和`ratios`的取值，观察生成的锚框的变化。\n",
    "* 构造交并比为0.5的两个边界框，观察它们的重合度。\n",
    "* 按本节定义的为锚框标注偏移量的方法（常数采用默认值），验证偏移量`labels[0]`的输出结果。\n",
    "* 修改“标注训练集的锚框”与“输出预测边界框”两小节中的变量`anchors`，结果有什么变化？\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "## 扫码直达[讨论区](https://discuss.gluon.ai/t/topic/7024)\n",
    "\n",
    "![](../img/qr_anchor.svg)"
   ]
  }
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